Reference no: EM133774009

Systems Thinking for an Integrated Workforce

Question 1 - Process Capability and the Taguchi Loss Function

ARGO Industries produces metal coils (springs) with specification limits for spring elongation (under a stretching force of 3 Newtons) of 13.00 cm ± 1.00 cm. Data for the elongations in a sample of 50 springs are in the JMP file ARGO.jmp (available on Canvas).

Construct a histogram of the data and obtain the capability indices Cpk and Cp. Include the histogram and state the values in your response, and identify, with rationale, which of these two measures would be more appropriate given the data at hand (max. 40 words).

JMP computing notes:

Use Analyse®Distribution to obtain the histogram.

In the resulting output click on the red arrow beside the word ‘Elongation' and select ‘Display Options > Horizontal Layout' in order to rotate the histogram.

Click again on the red arrow beside ‘Elongation' and select Capability analysis. You will be prompted to provide the lower and upper specification limits and the target value. Enter them and click OK.

i. State the loss function for this process based upon specification limits only, where the cost for rejecting a spring is $10.00;

ii. State the Taguchi loss function for this process, given loss = $10.00 at lower and upper specification limits (show working where applicable).

NOTE: JMP is not required for part b).
The mean of the sample is not at the target of 13.00cm but instead is 13.348. We can adjust the data to have a mean of 13.00, without changing the standard deviation, by subtracting 0.348 from every value. To do this, create a new column in the JMP file (called ‘Adj Data') containing a formula, ‘Elongation-0.348' (i.e., Elongation minus 0.348).
NOTE: We aren't altering or improving the process, we are simply adjusting the data so we may consider the situation where the process had the desired mean of 13.00 and the same standard deviation as the current process.
JMP computing notes to enter the formula ‘Elongation-0.348' in ARGO.jmp:
Select ‘Cols' from menu, then ‘New Column...'. Rename ‘Column 2' as ‘Adj Data', then click ‘OK'.
Click the right mouse button at the top of the column named ‘Adj Data' and select ‘Formula...'. This will take you to the formula window.
In the formula window, Click on ‘Elongation' at the left of the window then subtraction sign (-) then type
0.348 and press ‘Enter' key. Then click on ‘OK'.
I will assume that after completing this part of the question that you will have two columns of data, the original data called ‘Elongation' and the adjusted data called ‘Adj Data'.
Calculate the average Taguchi Loss per unit based on:
the original data (‘Elongation'); and
the adjusted data (‘Adj Data')
State the above two values. Do not provide a printout of your data or loss values calculated in JMP.
Compare the two values, commenting on what they demonstrate and any notable aspects in the context of this scenario. (max. 50 words)

JMP computing notes for entering formula for Taguchi Loss Function (TLF):
The following JMP commands provide the steps for placing a TLF formula of the form 20*(Elongation-15)2 in a column using the data in the column ‘Elongation'.

Create a Column 3: select ‘Cols' from menu, then ‘New Column...'. Rename ‘Column 3' as ‘TLF_orig_data' (short for TLF based on the original, unadjusted, data in the column named Elongation), click ‘OK'.
To enter the afore-mentioned example formula, 20*(Elongation-15)2 , click the right mouse button at the top of the column named ‘TLF_orig_data' and select ‘Formula...'.
In the resulting formula window:
Type 20, press ENTER
Click on the multiplication sign (x)
Type left bracket (from keyboard, i.e., SHIFT 9)
Click on Elongation (as this is the column containing the measurements) at the left of the window
Click on the minus sign
Type 15 and hit ENTER
Highlight (select) the bracketed section, including the brackets, by clicking on the right-bracket (a blue rectangle should surround the bracketed part), and then select the xy button in the window.
Type 2 and hit ENTER
The formula 20*(Elongation-15)2 is then entered. Click on ‘OK'.
Reminder - the above is to assist you with the process for entering such a formula - you must instead enter the TLF formula that you calculated in part b) ii.

To find the mean of TLF_orig_data use Analyse®Distribution.
Now create a Column 4 and repeat the above but replace ‘Elongation' with ‘Adj Data' in order to get the average Taguchi Loss per unit for the adjusted data. You might name Column 4 ‘TLF_adj_data' (as it is the TLF based on the adjusted data).
Check, by substitution and comparison, whether the average Taguchi Loss per unit for the original data is approximately equal to (show your working):
k (mean - target)2 + k (variance)
where k is the constant used in the Taguchi Loss Function; mean is the mean of the data;
target is the target value; and variance is the variance of the data.
JMP computing notes:
You can use the output from Analyse®Distribution to obtain the variance.

i. Based on the formula in part d), the loss consists of 2 components: a loss due to not centring the process on the target and a loss due to the variation in the process. For this example, which component is greater (support your decision, no marks can be awarded for simply stating ‘variation' or ‘not centring')? (max. 40 words)
ii. What does this scenario exemplify when considering process improvement? (max. 30 words)

Question 2 - Seven Simple Tools
For each scenario, identify which one of the ‘Seven Simple Tools' would best address the question or request. Name the tool and illustrate (sketch/draw) how the tool will look (show key features and some content for illustration purposes - adequate to demonstrate the tool's appearance, nature and keyfeatures, but not necessarily a comprehensive application of the tool to the scenario).
Notes:
You are not required to collect or locate any data.
If required to demonstrate a flow chart you should show some consideration of the structure, perhaps first few steps (similarly for Ishikawa diagram show basic structure); however, you aren't expected to provide the level of content detail the Assignment 1 response required - simply enough to show you have chosen the correct tool (not just by name) and that it would demonstrate to someone possibly unfamiliar with the tool the key aspects to include.
The senior manager in an insurance agency asks you, ‘How doesour administration department deal with written complaints from our customers?'
The regional manager calls to ask you to send a report clearly identifying the primary and other (in terms of frequency) types of banking errors that occurred at your branch the past financial year.
The General Manager of Woolworth's asks you to assess whether there is a relationship between the time customers spend waiting in line at the supermarket checkout (cashier) and the number of checkouts open.
Trainees are timed to see how long it takes to assemble a computer component. Graphically present the times (in seconds) that fifty trainees in an electronics training course each took to assemble the computer component (i.e., there are 50 recorded times).
In the airline industry, your manager asks you to simply present the distribution of the number of pieces of luggage (per million opportunities) misplaced per month by the sub-contracted baggage handlers.

What role does the ‘Seven Simple Tools' as a group play in facilitating quality improvement in an organisation, why are they useful? (max. 120 words) You may answer in point form. Refrain from describing each tool.

Question 3

After a concerning number of Lost-Time-Injuries (LTIs), an Australian Mining Company commenced an investigation into local work practices in an attempt to improve workplace safety. Over a 20-day period, a supervisor collected daily data on the number of employee-reported near miss incidents (NMIs)* along with a number of other factors, such as maximum temperature, tonnes mined, size of the work crew, and so forth.
* NMIs refer to unplanned and undesirable observations and events (including noted hazards) in the workplace that have the potential to cause, but haven't actually resulted in, workplace-related injury, damage or interruption to normal operation; employee-reported NMIs refer to a system whereby employees are requested to lodge details online should they happen to notice a NMI in the workplace.
A subset of the data is provided in the JMP file Incidents.JMP (available on Canvas). An excerpt of which appears below:

Provide three visual displays (one for each of the three variables, NMIs, Max Temp and Tonnes) of the time-ordered data(using one of the sevensimple tools) and comment. (max. 40 words - in total across all three visual displays)
To consider whether the daily number of NMIs reflects common cause variation, create a control chart for the NMIs per the following:
Construct an Individuals Chart for the data and simply provide this as your response.
JMP computing notes:
Select Analyse®Quality and Process > Control Chart > IR.
In the resulting window, place the variable ‘Near Miss Incidents' into the role of ‘Process'. Click OK.

From those presented in the course lectures, construct another control chart that would seem appropriate for the NMIs data.
Comment on the values of the key parameters (the centre line, the LCL and the UCL) in the Individuals and other control chart you have chosen, why the two charts' limits differ and which chart would be the more appropriate, with rationale. (max. 120 words)
Ensure you include the additional chart.

Does there appear to be a relationship between the NMIs and each of temperature and tonnes? Include evidence in the form of appropriate visual displays and measures. (max. 30 words)

NOTE: If you wish to use JMP to produce some output but are unclear on the commands to do so, you may approach me by clearly articulating what you wish to produce and I will provide the commands (provision of such commands is not necessarily an indication of appropriateness).

Provide a brief and informative summary report based on the analyses across parts a) - c). Within such, consider and comment on: whether there is any evidence to suggest that the potential for LTIs (not NMIs) is increasing; and any implications regarding knowledge around LTIs. (max. 150 words)